Puddle Locator (03 August 2024)

One night as I did my laundry, with confidence that the process needed no supervision I went to a different room to do something else expecting the usual audio notification I’d get when the process is complete. Sadly I’m about as sharp as a marble so I totally forgot about the task I had initiated in the other room. After a while, to my horror when I put my foot on the floor I felt a soggy carpet. A water supply pipe had unfastened from the machine and the water pump supplying the machine was gushing out water at a furious flow rate. Looking back at the incident I thank God the power extension bars that were on the floor miraculously did not have the water touch their live components. It could have meant electrocution or some other catastrophic outcome for me and other people in the house.

I got to thinking about how this hazard could occur in other settings especially in factories where they might work with high electrical power and processes that involve liquids that could leak and go undetected long enough to cause a cataclysm. So I brainstormed ideas on instrumentation to instantaneously detect the slightest liquid spillage on a surface such as a residential or factory floor. As a matter of course it’s installation in extant buildings would need to be straightforward. Maybe the system could also be installed on the bases of machinery. I suppose such a scheme could aptly brook the appellation “Puddle locator” but let’s give it the handle “Rover”.

After visualising a number of deployments for Rover I chose one in which the sensors would be distributed along strips fixed to the base of skirting-boards around the perimeter of the room. I thought of a scheme where we’d send out energy that would interact with the puddle in a way that sensors could then use to outline the location and geometry of the puddle(s). My mind kept coming back to electromagnetic waves. Picking up a book on electromagnetism the electromagnetic wave concepts I found appropriate were Snell’s laws of reflection and refraction. 

Fig. 1 Illustration of Puddle Location Scheme

I thought, the simplest approach (illustrated in Fig. 1) would be to use laser transceivers for the sensors. Rover would successively select a location of a transceiver from one end of a wall, e.g. starting from s₀ on wall-A moving towards s_c in Fig. 1. In Fig. 1 the transceiver s₁₁ is the current selection. So s₁₁ fires a beam in a direction normal to it's front face. If it receives a reflection this would imply the beam it sent out was at normal incidence with a body directly ahead of it. In that case Rover would then sequentially activate transceivers s_j>11, i.e. transceivers after s₁₁, to fire highly focused laser beams at angles, θ_s, with 0 <  θ_s < 90°. Rover will have the luminescent transceiver change the direction of it’s beam in discrete increments for θ_s. At each value of θ_s that the beam is fired if any of the transceivers, s_{j < 11}, receives a reflection of the beam (which should be at the known frequency of Rover transceivers’ light beams) it interrupts Rover’s scanning process. In the instance illustrated in Fig. 1, transceiver s₉ would interrupt Rover. To verify that the event can be used to calculate the proximity of the body to s₁₁ Rover will check if Snell’s law of reflection is satisfied, i.e. if 

To do that it simply checks if d_i = d_r. If this is true then Rover may proceed to compute the proximity, x, of the body’s edge to s₁₁ using the equation

Now, to check if  the body reflecting the light is a puddle of the liquid of interest Rover will resort to Snell’s law of refraction, 

In that effort, in the scenario depicted in Fig. 1 after calculating x Rover will continue from s₁₃ towards s_c activating the transceivers to look for a condition in which a critical incidence angle,  θ_c, is found. At this critical angle the transmission angle, θ_t  = 90° so a transceiver, s_cr, on wall-B will receive a transmitted beam from transceiver s_c and interrupt the scan. From equation (3) it follows that 

where 𝛍_L and 𝛆_L are, respectively, the permeability and permittivity of the liquid we’re attempting to detect and 𝛍_A and 𝛆_A are permeability and permittivity of air. So if Rover checks and finds that equation (4) is fulfilled then the body transmitting the beam is indeed a puddle of the liquid we’re scanning for and Rover logs the value of x (found earlier using equation (2)) as a point on the edge of the puddle.

If Rover conducts this ritual for all locations of transceivers on all walls of the room it should be in a position to  profile the location and geometry of all puddles on the floor. With extra development effort Rover could be designed such that when it detects a puddle it can then serve use cases such as displaying detailed visualisation of these puddles on a monitor and / or sounding an alarm.

But the thing to note is, with the requirements given above a primary consideration is that physical obstacles between the transceivers and the puddle may be an impediment if the electromagnetic waves require line of sight, for instance when using light as in my proposal. The same holds when using  electromagnetic waves of any other frequency if the obstacles are good electrical conductors.

Nonetheless, unless the obstacles completely surround the puddle we may at least detect the presence of the puddle though our apprehension of it’s full extent and geometry might not be accurate. This should still be good enough for an alarm to be raised by Rover.